Question: Simplify the following expression: $ y = \dfrac{3}{5} + \dfrac{3q}{3q - 2} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3q - 2}{3q - 2}$ $ \dfrac{3}{5} \times \dfrac{3q - 2}{3q - 2} = \dfrac{9q - 6}{15q - 10} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{3q}{3q - 2} \times \dfrac{5}{5} = \dfrac{15q}{15q - 10} $ Therefore $ y = \dfrac{9q - 6}{15q - 10} + \dfrac{15q}{15q - 10} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{9q - 6 + 15q}{15q - 10} $ $y = \dfrac{24q - 6}{15q - 10}$